OFFSET
0,3
COMMENTS
A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 7 with exactly one descent. For example, sigma can be chosen to be 1247356, 2413567, 3671245, 5712346, etc.
LINKS
Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = 1 + Sum_{i=2..6} binomial(n, i).
a(n) = A008859(n) - n.
G.f.: (1-6*x+16*x^2-23*x^3+19*x^4-8*x^5+2*x^6)/(1-x)^7.
E.g.f.: exp(x)*(720 + 360*x^2 + 120*x^3 + 30*x^4 + 6*x^5 + x^6)/720. - Stefano Spezia, Apr 20 2023
PROG
(PARI) a(n) = 1 + sum(i=2, 6, binomial(n, i)) \\ Andrew Howroyd, Apr 20 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jessica A. Tomasko, Apr 20 2023
STATUS
approved